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Algorithms and data structures for multi-adaptive time-stepping

Journal article
Authors Johan Jansson
Anders Logg
Published in ACM Transactions on Mathematical Software
Volume 35
Issue 3
ISSN 0098-3500
Publication year 2008
Published at Department of Mathematical Sciences, Mathematics
Language en
Links dx.doi.org/10.1145/1391989.1391990
Keywords Algorithms , C++ , Continuous Galerkin , Discontinuous Galerkin , DOLFIN , Implementation , Individual time steps , Local time steps , Mcgq , Mdgq , Multi-adaptivity , Multirate , ODE
Subject categories Mathematics, Computational Mathematics

Abstract

Multi-adaptive Galerkin methods are extensions of the standard continuous and discontinuous Galerkin methods for the numerical solution of initial value problems for ordinary or partial differential equations. In particular, the multi-adaptive methods allow individual and adaptive time steps to be used for different components or in different regions of space. We present algorithms for efficient multi-adaptive time-stepping, including the recursive construction of time slabs and adaptive time step selection. We also present data structures for efficient storage and interpolation of the multi-adaptive solution. The efficiency of the proposed algorithms and data structures is demonstrated for a series of benchmark problems. © 2008 ACM.

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